Menu

Month: February 2017

Various connotations for an alliterative Monday morning come to mind! One is that great song “Monday, Monday” by The Mamas and Papas (https://m.youtube.com/watch?v=iIo8_bMFwxs or https://m.youtube.com/watch?v=-TFddCrHlPY) I remember driving to back in the 60s, sometimes from my home in Tottenham into central London in the days when you could park free in the old Covent Garden, near King’s College in the Strand.

But today must be Morbid Monday as I scan the Obituary column in today’s Telegraph. I read with a little sadness but some amusement the coverage of Peter Skellern. It states that for a few years in the 80s he had a creative partnership with Richard Stilgoe, and one of their songs was “Joyce the Librarian”, who had never been kissed but had a liaison with a regular reader, and ended up like one of his library books – two weeks overdue.

Further down the page is the (appropriately enough, late) news of the February 6th death of Raymond Smullyan, a mathematician, logician, and sometime magician and pianist whom I remember from one or two of his mystifying (mathematical) publications from my time as a research student in the late 60s. I still have his arcane book “Theory of Formal Systems” which I think I acquired from attending a summer school at Prof Chris Zeeman’s Maths department in Warwick, where my bestie Maths pal, David Fallows was an MSc student, after our first degrees at King’s.

Smullyan’s obituary (pictured here) mentions one of many logic problems he published over the years, including in several high-end puzzle books. It presents you with three gods A, B and C, who, in no particular order, are called Truth, False and Random. True always tells the truth, False always speaks falsely and whether Random speaks truly or falsely is a random matter.

Your task is to determine the identities of A, B and C by asking three yes-no questions, each one of which is addressed to only one God, although you may ask the same God more than one question.

The Gods understand English, but their answers are given in their own language; their words for “yes” and “no” are “da” and “ja” although you don’t know which is which.

There are online solutions for this, but give it a try first, before looking. (This is my return shot, Tom, for the polynomial question you set me!)

There is a simpler problem of this kind: you are at a fork in the road, and there is a person there from the local community, which comprises people who either always tell the truth or always lie. You may ask just one question to the person there to establish which way to go to your desired destination, but you don’t know if you are speaking to a truth teller or an inveterate liar. What would you ask?

Well, today’s obituaries have inculcated more than just the usual regret! Mostly, in reading obituaries (as I have tended to do for many years) I have been inspired by the many achievements of those who have been their subject. Over their lifespans, so many people have achieved so much!

I hope my interlocutor, when the time comes, can be creative in this respect!

John Wheeler had a great way of explaining both special and general relativity, and any of his books is worth the time spent to read them. Find this quote in his “Geons, Black Holes, and Quantum Foam”. He also came up with the terms “Black Hole” and “Wormhole”.

Depending on your grasp of the mathematics, a good book to start with might be his book written with Edwin Taylor, first edition in 1965, Spacetime Physics.

A much more demanding book from 1973 is “Gravitation”, a classic written with Charles Misner and Kip Thorne, which as its title implies covers General Relativity (i.e. relativity WITH gravity).

Of course, we hardly see space-time curvature in our day-to-day lives, just as we hardly see the direct effects of special relativity (although our lives depend on it in many ways at the subatomic level). Newtonian mechanics is a very good approximation for our everyday purposes.

But in high field strength gravitational fields, light will follow a curved path because in effect mass and space-time curvature go hand in hand. And at the special relativistic level (no gravity), at speeds near to the speed of light, physical effects are measurable such as time dilatation and length contraction.

These effects sound very odd, but given that a major axiom of relativity theory is that light always passes us at the same speed, no matter the velocity of the light source, any consequences are bound to be counter-intuitive. Our everyday experience is that, for example, a cricket ball bowled or thrown at us by someone running towards us is endowed with their running speed plus the speed of their arm. A ball thrown from a standing position with the same throwing or bowling action will be slower.

At speeds near to the speed of light (“relativistic” speeds), however, this additive “cricket ball” effect breaks down, and for light itself there is NO added speed if the source is moving towards us, even if the source is travelling at nearly the speed of light. (On a related point, light from distant sources in the Universe, travelling away from us very quickly, passes us at that same light speed, but is red-shifted. An interesting debate is to read Fred Hoyle on why there is so little blue-shifting, but that is a whole other discussion!)

Similarly for gravitation fields – it is only when the field strength is very high can we detect the predicted effects. The “lensing” or convergence of light from behind a massive star (like the sun) or the recent ground-breaking detection of gravitational waves thought to be issued by a pair of rotating black holes (the LIGO experiment) depend on very high gravitation fields we simply don’t encounter here on Earth.

General Relativity was used to calculated a predicted precession of the orbit of Mercury distinct from the Newtonian calculated precession – and it was found to agree with observation. But even that closely to the sun, the effect is tiny and would hardly have been noticed but for the intense scrutiny that was made as a test of Einstein’s theories.

Einstein’s creativity in postulating the constancy of the speed of light, and then his doggedness, using the mathematical tools then at his disposal (i.e. not our modern more evocative nomenclature and terminology that is more revealing of patterns in the required algebraic geometry) in solving the general Relativistic field equations show both his abundant inspiration, and lots of perspiration.

After all, to return to Wheeler’s duality of mass and spacetime geometry (curvature), for Einstein to solve equations that are reflexive in that the “independent” variables are also “dependent” is much harder than when you can assume that one set of variables is fixed and the others’ movement or variation doesn’t affect the first.

(Physics and mathematics are rich with examples of simplifying assumptions to help solve problems (often “linearizing” non-linear differential equations). For example, the general “three body problem” in Newtonian gravity is intractable, but the “reduced” three body problem (RTBP) IS tractable, the simplifying assumption being that one of the three bodies is postulated to be so small (e.g. a satellite in the presence of the earth and moon) that although it is affected by the gravitational field of the earth and moon, it has no effect itself on the sun and moon. In this way the problem is sufficiently decoupled (or linearized”) to be solvable).

100 years later Einstein’s theory still stands up. Probably quantum theory, and the union of it with General Relativity to create a GUT – a Grand Universal Theory – whether through string theory (maybe not) or loop quantum gravity (maybe) or some other yet to be fully formulated process will turn General Relativity into a “good approximation” just as Newtonian theory is a good approximation to relativity. Again Wheeler’s “Geons, Black Holes, and Quantum Foam” provides some food for thought.

But just as Newton loses none of his reputation as a giant of physics of his time, following Einstein’s work, neither will Einstein lose his as a result of any new all-embracing theory. They both had broad enough shoulders for others to use to develop our scientific understanding.

Is space-time real?

Einstein’s space-time is a mathematical construct to allow him (and us) to understand how space and time have to be inter-dependent. Look up the definition of “simultaneity” in the special relativity context, and you will see that simply modelling space and time separately with no interaction between them fails to allow for the fact that different observers moving at different speeds will disagree about whether events that happen that are spatially separated are simultaneous, or whether one event happens before the other. All three outcomes are possible depending on the speed and direction of motion of the observer, and this can only be postulated and resolved with a space-time model, NOT in a model with a fixed time axis. All this tells us that space-time IS physically real, in that the effects we would see if velocities were high enough are genuinely predicted and correctly calculated in the space-time model. Our lives are played out in such a definition of the interdependency of space and time, not in a fixed three dimensions with a fixed and separate time dimension shared by everyone. In the language of the theory, we all have our own “world-line” that is a combination of where AND WHEN we “are”, and these world lines have their own individual pace of time (not one shared by all), and at high speed differentials mean that we, and others, might observe events, as discussed above, happening in a different order from each other. There are limitations on how much and if these differences occur, depending whether the separation of space-time location of the events we are observing are “space-like” or “time-like” but Quora isn’t a great medium for illustrating that. But I can elsewhere is needed!

Now that my son Tom will be ski-leading for the Ski Club of Great Britain in Verbier later this month, including some off-piste days, or at least with a greater proportion of off-piste than our usual family skiing, my mind turns towards avalanche safety and the recent sad news of the fatal avalanche in a familiar resort we have skied in many times, Tignes (and Val d’Isère).

The first news of this was on the BBC and Sky News websites. The BBC coverage at http://www.bbc.co.uk/news/world-europe-38954628 has been updated to reflect the later news that the group, which included a 48-year-old man, his 15-year-old son and the son’s 19-year-old half-brother, as well as the experienced and well-known instructor, 59, were only a few dozen metres from the ski lift. It would seem they had been walking, carrying their snowboards, possibly towards a nearby lift. Since they were swept 400m down the slope, this must have been higher up, perhaps the Combe Folle draglift up to just below the top of the Lavachet Wall.

The Sky report, that hasn’t been updated, said the avalanche had been in the Tovière area. I well remember the run Mur de Paquerettes (https://m.youtube.com/watch?v=QuwFfN6ESqo) (PS not me skiing in this video) underneath the Tovière mountain restaurant, where there is live music and where the hang gliders take off. Mur de Paquerettes is a pretty steep mogul run we have skied a lot, but it isn’t in the pictures here; we don’t see the Tovière Gondola bubble lift which provides a spectator view of the mogul antics from right over the run. It is further to the right as we look here; the off-piste run in this avalanche area is down from the Lavachet Wall, and we see part of Tignes le Lavachet in the foreground.

These screenshots from the excellent ski navigation app FatMap (https://fatmap.com) show the area concerned. In the lower centre of the right hand picture, we can clearly see the large ridge that protects the Tignes village of Le Lavachet, with a smaller similar feature protecting Val Claret pictured at the centre of the wider shot on the left.

Tovière ski area in Tignes, showing Val Claret where run Mur de Paquerettes and Henri end, both away from the affected area

Tovière ski area at Tignes Lac and Le Lavachet, where the affected off-piste runs and the avalanche end. Note the avalanche barriers

This extract from the Tigne piste map shows the specific area concerned and the ridge clearly visible to the left of Le Lavachet. Note that the red piste Combe Folle, and the black runs Crocus and Trolles finish at the Tignes Lac and Le Lavachet side.

Tignes piste map showing the local lifts and pistes above Val Claret, and near the affected area above Lac and Le Lavachet

Henry “Avalanche Talk” Schniewind was interviewed this morning about yesterday’s avalanche in Tignes down from the Lavachet wall. This is clearly an historically avalanche-prone slope, so much so that the man-made ridge and trough seen above had been constructed to protect houses in Tignes Le Lavachet from avalanches, and the party were thus caught in even deeper snow in the trough or gully between the slope itself and the ridge. Estimates of the accumulated avalanche depth there range from Henry’s 2-3 metres to 8 metres in the BBC report. Not a great place to be skiing (or even walking, as this party were thought to have been, carrying their snowboards towards a nearby lift) between a steep slope above and a snow trap below. It is to be remembered that once the avalanche snow stops moving, it has the consistency of concrete, rendering it vital to somehow stay on top of – or float on – the avalanche as it is moving down the slope, before it comes to a stop.

Here is the weblink for this morning’s ITV interview with Henry Schniewind:

Henry talks about the vital, minimum equipment necessary when skiing off-piste – an avalanche transceiver, a probe and a shovel. To this many would nowadays add a flotation air-bag rucksack, although opinions are divided on this. Opinion is also divided on which type to choose – a mechanically triggered RAS system (e.g. Mammut), an electronically triggered ABS system (e.g. Ortovox) or an electric fan-based inflation system (such as the Black Diamond Jetforce system), which obviates any (compressed air cylinder) issues for air travel with such rucksacks, but which might not be so quick or effective for inflation. All types are triggered by the wearer using a T-handle, stored in the rucksack shoulder strap when not required.

There was a lot of confusion on the scene of the Lavachet Wall avalanche yesterday but clear details have finally emerged.
The group taken by the slide was a group of 4, and not of 9 as previously reported. It is currently not clear why authorities were looking for 9 victims – it sounds as if the family party of four were all double booked.
The instructor was a very high-level ESF snowboard instructor, aged 59, with years of experience. His clients were a family from the South of France: a father, 48; his son, 15; and his step-son, 19 – all strong snowboarders, all wearing avalanche kit. One member of the family escaped having descended earlier with an equipment issue.
The slide took them while they were boot-packing across the face which cut in to the snowpack, weakening it, and causing the slide to release. 40m wide at its release point, the avalanche took the victims over 400m down the slope burying them underneath 7m of snow in a man-made gully built for the express purpose of protecting the houses behind it from avalanche debris.
With Météo France’s avalanche bulletin warning of windslabs and instability on slopes of this aspect an investigation will follow. Jean-Christophe Vitale, the mayor of Tignes, has gone on record to say: “He was a very experienced professional who knew the area well. I’m sure he took every precaution while taking his clients to this place, but off-piste zero risk does not exist.”
One bright-side to the incident is that one 16-year-old who was with the group when they did the same run earlier in the morning wasn’t with them on the second run. Either experiencing problems with his equipment or after a fall the instructor sent him down the pistes for the day. It wasn’t until the afternoon that he learnt the group he was with were caught in the slide.

Hero image: Radio Val d’sere, Graphic: LP/INFOGRAPHIE

The risk of avalanche at the time of the avalanche was 3 on the scale of 5 and this incident, on a North-West facing slope, came on a relatively warm morning after several days of strong winds. Météo France’s official avalanche report noted the risk of rising temperatures and the presence of wind slabs on North, West, and Southerly aspects.

An avalanche risk rating of 3 is hardly unusual through the season; it highlights the need to be very aware of the weather reports and resort assessments, noting that there is always some risk. Here is that morning’s Metéo France report:

Météo France’s official avalanche report

The following article by Henry Schniewind and Hugh Morris has some useful hints and tips on what to keep in mind when skiing off-piste:

On the lost ride retrieval topic, I haven’t yet found a way to locate any surviving Tacx data from my iPad, but I have several times had cause to edit a Garmin ride file which wouldn’t upload to Strava.

Typically this has been because the ride data file has been corrupted, albeit quite innocently. On one occasion I paused my Garmin 705 and paused/unpaused it several times too rapidly to make sure I was hearing the right chirp or multiple chirp which indicates it is running (or not). This cause the file to be mis-recorded – I’ll come to that in a moment.

The most recent occasion was with my Garmin 520, which just switched itself off mid-ride. I turned it back on, and the ride appeared to be recorded normally, but would also not upload to Strava. On the 520, as with the more modern Garmin devices, it looks to an iPhone using the Garmin Connect app and bluetooth, and this ride would not synchronise to the phone either.

On both occasions I was able to repair the file using TextWrangler, an advance text editing application (on my MacBook Pro) that I use to create and edit web pages. It handles a file structure called “XML”, a structure that on a line by line basis creates tagged files that contain data in a repeating pattern enclosed by an open and closing tag for each data item such as heart rate, latitude and longitude and so on. Here is an example of two successive “Trackpoints” that the Garmin records every second or two during a ride:

The problem with the Garmin 705 failure was just that ONE of the opening tags <Trackpoint> was missing for one timestamp, so that the file was formatted incorrectly. Strava is VERY strict on accepting only correctly formatted files, so until I added this tag back in (there are thousands of them in any ride, 20,000 in that particular ride) Strava wouldn’t accept it; but even replacing just that one missing one meant that I could use the file for Strava.

On the second occasion with the 520, one timestamp at the point that the Garmin 520 turned itself off suddenly changed its date to a completely different day, and all the rest of the dates were similarly wrong for the rest of the file. Here are the two successive timestamps in question, with a sudden jump from 2016-11-27 to 2019-04-07! This was at line 23857 out of 84192 in the file altogether:

This time, a simple global edit to make all of those (10,000) subsequent dates the same as the first 5,000 or so meant that the file was once more readable by Strava. In this case, Garmin Express on the MacBook WAS able to read the original file, as no doubt Garmin’s software is better at second guessing their own software glitches than Strava is, or is bothered to be! In general I find Garmin’s software leaves a lot to be desired, both on the Mac and also in their devices, but the 520/820 series are a lot better than previous models.

One final point: .fit files that are created and used by those more modern Garmin devices are not alphanumeric, so they aren’t easily correctable other than wth Garmin’s own web-based available software, which just tends to truncate any part of the file that has an error. But if you can read the file with the laptop applications Garmin Express or Garmin Basecamp, you can the export a .tcx or.gpx file from them which IS the tagged file structure you can edit in an application like TextWrangler. The .fit files don’t look very amenable in Textwrangler – ouch!:

Recently I have lost or partially lost Tacx rides using their trainer software on my iPad, and also had one lost Zwift ride.

For Zwift there is a way to recover partial rides if the software freezes, by peering into the iPhone or iPad with a laptop program called iMazing. It’s a chargeable program, but has a set of free functions which are enough to bring up the Zwift/activities folder in the iPad, from where stored .fit files – and also image files if you have taken screenshots – can be copied to upload manually to Strava.

The Tacx Flow, and other smart turbo trainers transmit and receive on Bluetooth as well as ANT+. So for a handheld or laptop with Bluetooth you should be OK with a smart turbo (although there does seem to be a Tacx limitation on the number of ANT+ channels available such that if using a Garmin GPS AND a laptop, one must be on Bluetooth if the other is on ANT+ dongle connection, or two dongles are required).

A heart strap would also need to transmit Bluetooth, though, if there is no ANT capability on the training software device, so for example if it’s a Garmin HRM that only sends ANT+ you’d need the dongle. I bought a dual HRM (sends both ANT+ AND Bluetooth) on Amazon called Coolspro, but I’m sure there are others.

I think a watch that measures and sends HR might work as well. Only issues with an ANT+ dongle for a handheld Apple device are a) that mine (the Wahoo dongle) is designed for the older, larger lightning socket, so I also had to buy an adapter to connect into the current small lightning socket in the Apple handheld; b) the size of the older lightning plug means I have to take the cover off my iPhone or iPad to get it fully in; and c) the device’s power socket is also the lightning socket, so if using the dongle you have to make sure the handheld is well charged before the turbo session. All in all, it’s better to use Bluetooth, which I have found has less dropouts, that are REALLY annoying as all ride data gets lost.

I now use a piece of MacBook s/w called iMazing that lets you find files inside an attached iPad or iPhone, and even incomplete Zwift .fit ride files are stored in the Zwift/activities folder that you can find in iMazing, copy over to the MacBook and then upload to Strava as a manual entry. Any screenshots you take during a Zwift ride are there too. I haven’t found a way of doing that for incomplete Tacx rides. Btw Tacx have a cloud site https://cloud.tacx.com where all your completed rides CAN be uploaded by default so you never lose a ride even if you lose your handheld!

This little video shows three possible paths – the straight line (the shortest), a path that descends quickly and then becomes flat as it gets to the destination, and one in between, looking more elliptical* in shape.

Ever wondered what downhill profile of road will get you most quickly to the bottom of the hill freewheeling from a given point T (the top) to a given point P (the pub)? Now you know – it’s a cycloid, appropriately enough. Now I just need to think about the best shape of road from the pub to the top for the fastest ascent for a given a) wattage, and b) for a given pedal pressure…

Even more arcanely (I was going to say more interestingly, but I’m realistic about reading endurance!) the cycloid, as the second article says, is isochronous. It means that even if you start freewheeling from a rest position R half way down the hill, it still takes the same time to get to the pub. Why? Briefly, because starting higher up, at the intermediate point R you are moving, whereas starting from R you are at rest. Weird, huh? It’s the same for any point R, no matter how close to the pub.

*the elliptical path is nearly as fast as the cycloid – but not quite!!

I have another interesting quirk to discuss with you relating to my Tacx Flow turbo, or indeed any other Tacx turbo that has a relatively low maximum slope simulation capability (i.e. other than the Neo, i-Genius or Bushido) such as the Flow at 6% max or the Vortex at 7% max. This is from the Tacx support pages http://forum.tacx.com/viewtopic.php?f=213&t=25258:

“When a trainer cannot apply enough resistance, the measured speed does not comply with your exercise (training program) anymore.
To solve this the speed is calculated (Virtual Speed) based on the power you are producing and the exercise data (current slope).

“e.g. You are riding an exercise which consists of a single 10 % slope on a trainer which can only apply enough resistance to simulate a 7 % slope.

“Using measured speed you will finish the exercise much sooner compared to actually riding the same 10 % slope in real life, because the trainer cannot apply enough resistance causing you to go faster resulting in the exercise costing you less effort.

“Using virtual speed your exercise will be much closer to actually riding the same 10 % slope in real life, because it calculates how fast you would be going on a 10 % slope based on the effort (power) you are producing on the trainer

“Keep in mind speed shown in TCA is also NOT the raw speed from the trainer. It’s always calculated with the same virtual speed calculations but not flagged as virtual speed cause it’s less than 10% deviation from the RAW speed of the trainer.

“Measured speed from a sensor is treated as raw speed.”

So if you use a speed/cadence sensor with your turbo bike, you will get raw speed recorded, allegedly. I have certainly noticed downhill speeds being greater then I would have thought, and uphill speeds possibly slower (but then that may be my issue!)

On the retailer Wiggle’s site I see it asserted that apparently Zwift have partnered with Strava to allow virtual rides to count towards Challenges if you use such a sensor (as I am only riding turbo at the moment, I have zero distance and elevation in Strava Challenges for January, and probably December too). My personal targets are as normal. See:

Here’s a very interesting article with, for me, some initially counter-intuitive outcomes – until I thought about it more.

For context, I’m using the Smart Tacx Flow as an alternative to my non-Smart i-Genius trainer (a contradiction in terms…).. The Flow goes up to 6% incline and 750W. No motor for downhill, but it DOES reduce the flat riding resistance which can be felt to about 3% downhill, and then it stays the same. No motor means if I stop pedalling it eventually stops whether up or downhill. For my money it’s great value. I reckon it’s swings and roundabouts on 6% max and no motor compared to I-Genius. I work harder on big downhills but less hard on steeper hills. The Zwift “difficulty setting” offers a way to make the 6% hills and above feel tougher…

The article at http://zwiftblog.com/using-the-trainer-difficulty-setting-in-zwift/ describes resetting the resistance levels when using Zwift to increase or reduce the multiple of training effort for any given slope, WITH NO CHANGE TO THE WATTS REQUIRED. How can that be, one might ask? Surely, if you increase the resistance multiple for any hill, thereby increasing pedal pressure (the intention of the change (in my case) to circumvent the Flow’s 6% max slope simulation) then isn’t the power (pedal force X speed = work rate) increased, or do they reckon because you are likely to reduce cadence (for a given gear) as a result, the speed diminishes in proportion with the increase in pedal pressure?

Having a PhD in Theoretical Physics means I’m a little ashamed of myself even to have a momentarily different intuition initially! But people of my age who did Applied Maths at school ought to remember the old Horsepower formula HP = Pv/550 (in appropriate units). Power is proportional to the multiple of force P and velocity v. It’s why some sports car manufacturers used to be so fond of highlighting their cars’ horsepower, because by making their engines rev at very high revs (enhancing engine wear no end) they could advertise very high horse-power. Very UNusable power, given how high you had to rev in all the low gears to get performance. The American way was to make engines bigger and bigger (427 cubic inch (7 litre) V8 preferably) so that TORQUE (turning force) was very high and the engines were just ticking over at quite high speeds, generating power at much more usable revs. Even smaller diesels (whose fuel characteristic is different from petrol) produce high torque at low revs too, compared to lighter, faster revving petrol engines.

As for cycling, and using the Zwift “difficulty setting” to change the perceived resistance, I guess, as the article says, just like the automobile analogy, it’s really a cadence control. You push harder on the pedals, say, but at lower revs, so the power is the same. Watch those quads grow!

Having used the Tacx non-smart i-Genius turbo trainer for a while, I have also been using my Tacx smart Flow trainer a lot recently.

The Tacx Flow is great value, the lowest price Tacx trainer that is fully smart, i.e. ANT FE-C and Bluetooth bidirectional. Thus the trainer software (Tacx films or 3rd party like Zwift, on laptop or handheld device where applicable) will control the Flow brake, and the Flow sends all speed, power and cadence data to the training software.

You can also control a smart trainer like the Tacx Flow with the Garmin x20 series, i.e. such as the 520 or 820 that have the right data protocols.

At this low end of the Tacx range, you are limited to 6% uphill simulation and 750W power, but I don’t find this too much of an issue. Because it doesn’t have a motor to help simulate downhill freewheeling (like the I-Genius I also have) you work harder downhill to make up for it being easier at 7% uphill and above because the resistance is limited to simulating 6% max.

The Tacx Vortex does 7% and 950W but not worth quite a bit extra price in my opinion. I have published quite a bit on all this on Facebook to my cycling Club I have also described how Zwift offers the option of increasing what they call “difficulty” from the default standard 50% to something higher. This increases resistance on hills, lowering cadence and speed and leaving power the same.

Tacx have something called “virtual speed” which decreases reported speed uphill and increases it downhill to compensate for the maximum simulated uphill and downhills on trainers like the Flow and Vortex.